Deck 3: Parallel Lines

Question 1

Assuming that statements (1)and (2)are true, which conclusion completes the Law of Negative Inference? (1)P Q
(2)∼ Q

A)Q
B)∼ Q
C)P
D)∼ P

Answer 1

D

Question 2

If r || s and m = 73 ° , find m .

Answer 2

NOT ANSWERED.

Question 3

Two parallel lines l and m are cut by transversal t . For a pair of interior angles on one side of line t , the angle-bisectors are drawn to meet at point E. Find m .

A)45 °
B)60 °
C)75 °
D)90 °

Answer 3

D

Question 4

When two lines are cut by a transversal, and are one pair of alternate interior angles that are formed. If    and   , what relationship (in simplified form)exists between x and y ? Answer in the form x = .

Question 5

The statement, "The midpoint of a line segment is unique" is proven by the indirect method.

Question 6

If r || s and m = 108 ° , then:

A)m = 72 °
B)m = 108 °
C)m = 72 °
D)None of These

Question 7

Which statement would one prove by the indirect method?

A)If and are not congruent angles, then and are not vertical angles.
B)If r || s , then .
C)If l ⊥ m and m ⊥ p , then l || p .
D)If two sides of a triangle are congruent, then two angles of that triangle are congruent.

Question 8

Through a point not on a given line, there is exactly one line parallel to the given line.

Question 9

For parallel lines a and b , and are corresponding angles. If   and , find x .

Question 10

In (not shown), is a right angle. Where M is a point on and N is a point on , how are and related?

Question 11

Given that r || s and transversal t, ∠1 and ∠6 are supplementary.

Question 12

Which statement is a corollary of the theorem, "The sum of the three interior angles of a triangle is 180°."

A)Each interior angle of a square is a right angle.
B)Each interior angle of an equiangular triangle measures 60 ° .
C)The diagonals of a rectangle are congruent.
D)None of These

Question 13

Given line l, how many lines in space can be drawn parallel to l?

Question 14

When two parallel lines are cut by a transversal, and are a pair of corresponding angles that are formed. If    and   , find x .

Question 15

When lines a and b are cut by transversal d , and are a pair of alternate exterior angles that are formed. If and , find x .

A)x = 3
B)x = 3.5
C)x = 4
D)x = 4.5

Question 16

In the figure, and transversal t . If and , find x .

Question 17

When two parallel lines are cut by a transversal, and are a pair of alternate interior angles formed. If and , find x .

A)x = 5
B)x = 6
C)x = 7
D)x = 8

Question 18

Assuming that (i)and (ii)are true statements, what conclusion can you deduce?
(i)If x = 5, then x 3.
(ii)x 3

Question 19

If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are:

Question 20

Using the symbols ∼ (for negation)and → (for implication), write the contrapositive ofthe implication P → Q.

Question 21

Given two parallel lines, suppose that the bisectors of two interior angles on the same side of a transversal are drawn to meet at a point. Find the measure of the angle formed by the angle-bisectors.

Question 22

If and are both right angles, then one can conclude that:

A)a ⊥ b
B)b ⊥ d
C)a || b
D)None of These

Question 23

Given the coplanar lines and the fact that , which lines must be parallel?

Question 24

When two planes intersect, their intersection is a(n):

Question 25

Suppose that point P lies above line l. What is the first step in construction of a line through P parallel to line l?

Question 26

The statement, "If 2 parallel lines are cut by a transversal, then corresponding angles are congruent" can be used to prove that 2 lines are parallel.

Question 27

In the figure, a || b and transversal t . If   and   , find x .

Question 28

For coplanar lines r, s, and t, if r ⊥ t and s ⊥ t, then r || s.

Question 29

Suppose that . Which must be true?

A)a || b
B)a ⊥ c
C)c || d
D)c is not parallel to d

Question 30

If two lines in space do not meet, they must be parallel.

Question 31

If m = 57 ° and m = 123 ° , then r || s .

Question 32

In the figure, . If    and   , find x .

Question 33

If coplanar lines r and s are cut by transversal t so that alternate exterior anglesare congruent, then r || s.

Question 34

The indirect proof of the statement, "If is not perpendicular to , then ∠1 and ∠2 are not complementary" begins with the statement, "Suppose that ∠1 and ∠2 are complementary."

Question 35

Suppose that lines r and s are both perpendicular to line t. Then r is parallel to s if:

A)r and s are collinear
B)r and s intersect
C)r and s are coplanar
D)None of These

Question 36

Write the first statement of the indirect proof for this statement:"If coplanar lines l and m are not perpendicular to the same line t, then l and m are not parallel."

Question 37

When two parallel lines are cut by a transversal, what relationship exists between a pair of interior angles on the same side of the transversal?

Question 38

The measures of the three interior angles of a triangle are x, 2x, and 3x. What type of triangleis the triangle described?

Question 39

Given the coplanar lines and the fact that , which lines must be parallel?

Question 40

For lines l, m, and n to be parallel by pairs, the three lines must be coplanar lines.

Question 41

A pentagon has the same number of diagonals as it has sides.

Question 42

Find the measure of each exterior angle of a regular dodecagon (polygon with 12 sides).

Question 43

Draw a conclusion based upon true statements (i.)and (ii.).
(i.)If two triangles are congruent, then they are similar.
(ii.) is not similar to .

Question 44

If m = 37 ° and m = 76 ° in , it follows that m = 77 ° .

Question 45

In , m = 37 ° and m = 116 ° . Find the measure of exterior angle RTV.

Question 46

In , is a right angle. If m is 26 ° larger than m , find m .

A)26 °
B)32 °
C)42 °
D)58 °

Question 47

Each interior angle of a regular hexagon measures 60°.

Question 48

In , m = 84 ° and m = 42 ° . The bisectors of and meet at the point V in the interior of . What is the measure of ?

Question 49

For , there is an exterior angle at vertex Z . If m = 68 ° and m = 47 ° , find m .

A)65 °
B)68 °
C)115 °
D)125 °

Question 50

Find the sum of the interior angles of a hexagon.

A)180 °
B)360 °
C)540 °
D)None of These

Question 51

The polygon shown is concave.

Question 52

In , it is given that is a right angle. What word characterizes the relationship
between and ?

Question 53

What type of polygon has exactly 8 sides?

A)pentagon
B)hexagon
C)octagon
D)decagon

Question 54

In , = 47 ° , = 3 y - 7, and = 2( y + 10). Find the value of y .

Question 55

It is possible for a triangle to be both isosceles and obtuse.

Question 56

If a triangle has exactly two congruent sides, then it is an isosceles triangle.

Question 57

In , m = 37 ° and m = 53 ° . What type of triangle is ?

Question 58

In , m = 37 ° and m = 69 ° . Find m .

Question 59

As shown, must be an isosceles triangle.

Question 60

In ,   , , and . find .

A)20 °
B)40 °
C)60 °
D)80 °

Question 61

What two qualities are needed in order that a polygon be classified as a REGULAR polygon?

Question 62

Find the measure of each interior angle of a regular octagon.

A)45 °
B)108 °
C)120 °
D)135 °

Question 63

Of the upper-case letters R, S, and T, which one has line symmetry?

Question 64

Which type of figure has symmetry with respect to a point?

A)an equilateral triangle
B)any square
C)any pentagon
D)None of These

Question 65

If the word MOM is relected across a horizontal line that lies beneath this word, what word is formed?

Question 66

Which upper case letter has symmetry with respect to exactly one line?

A)F
B)G
C)H
D)M

Question 67

How many lines of symmetry does the square have?

Question 68

Any transformation of a geometric figure produces an image that is congruent to thegiven geometric figure.

Question 69

What is the specific name of the star-shaped figure that is formed when the sides of a convex pentagon are extended to meet at points in the exterior of the pentagon?

Question 70

Use to find the total number of diagonals for a polygon with 10 sides.

A)35
B)45
C)70
D)None of These

Question 71

Find the total number of diagonals for a concave hexagon.

Question 72

The figure (a square)shown has exactly one line of symmetry.

Question 73

Of the upper case letters R, S, and T, which one has point symmetry?

Question 74

The upper case H has point symmetry.

Question 75

Find the sum of the interior angles for an octagon.

Question 76

The number of diagonals D for a polygon of n sides is given by . Find the number
of sides for a polygon that has 14 diagonals.

Question 77

What does the letter D represent in the formula   ?

Question 78

A regular hexagon has a point of symmetry. What is the smallest measure for an angle of rotation that has the image trace (fall over)the given hexagon?

Question 79

For the triangle shown, what is the image of the reflection of the given triangle across ?

A)a right triangle
B)an acute triangle
C)an obtuse triangle
D)an isosceles triangle

Question 80

Assuming that a figure has point symmetry, what is the largest number of points of symmetrythat a figure can have?